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3 years ago

Please help with algebra question

Mathematics

1 answer:

Sunny_sXe [5.5K]3 years ago

4 0

We have that
5x+6y=10
4x+7y=19

using a graph tool
see the attached figure

Part A)
the solution is the point (-4,5)
x=-4
y=5

Part B)
we know that

If a system has at least one solution, it is said to be <span>consistent </span>.

If a consistent system has exactly one solution, it is independent

the equations are independent and consistent. Their graphs intersect at one point

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When 3.7 is added to 6 times a number the result is 52.3 find the number

cluponka [151]

(52.3-3.7)/6x

48.6/6x

x=8.1

Hope this helped :)

6 0

4 years ago

Find the missing side of a right triangle a b c

iren2701 [21]

Answer:

Use Pythagorean Theorem.

Step-by-step explanation:

To find any side of a right angled triangle, we use Pythagorean Theorem. It states that the square of hypotenuse is equal to the sum of squares of it's sides.

Let hypotenuse is a

Perpendicular is b

and base is c

According to the theorem:

a²= b² + c²

Add values and solve for the unknown variable / side.

If you had added the problem, I would have elaborated more but still this will help you out.

5 0

3 years ago

Read 2 more answers

Shawn is coasting down a 500 \text{ cm}500 cm500, space, c, m long ramp on his inline skates. The wheels on his inline skates ar

Nata [24]

Answer: 16 rotations

Step-by-step explanation:

Given : Shawn is coasting down a 500 cm long ramp on his inline skates. The wheels on his inline skates are 32 cm in circumference.

Length of ramp = 500 cm

Circumference of wheels = 32 cm

Formula :

Number of rotations = Length of ramp divided by Circumference of wheels

= 500 cm ÷ 32 cm

= 15.625 ≈ 16 [approx]

Therefore, each wheel makes 16 rotations while Shawn is coasting down the ramp.

5 0

4 years ago

3.48 An apartment seeker in Manhattan estimates that 10% of the available apartments in her price range are in acceptable condit

REY [17]

Answer:

a) 10 weeks

b) P(k≤2)=0.190

c) P(k>17)=0.167

Step-by-step explanation:

This problem can be solved applying the geometric distribution.

The probability of needing k weeks to find an acceptable apartment can be written as:

$P(k)=(1-p)^{k-1}p=0.9^{k-1}\cdot 0.1$

a) The expected value of this distribution is:

$E(x)=1/p=1/0.1=10$

Answer: 10 weeks

b) The probability of finding an acceptable department in the first 2 weeks is:

$P(k\leq2)=P(1)+P(2)=0.1*0.9^0+0.1*0.9^1\\\\P(k\leq 2)=0.1+0.09=0.19$

c) We have to calculate P(k>17)

$P(k>17)=1-\sum_1^{17}P(k_i)\\\\P(k>17)=1-(P(1)+P(2)+P(3)+...+P(17))\\\\P(k>17)=1-(0.1+0.09+0.081+0.073+0.066+0.059+0.053+0.048+0.043+0.039+0.035+0.031+0.028+0.025+0.023+0.021+0.019)\\\\P(k>17)=1-0.833=0.167$

6 0

3 years ago

One hundred teachers attended a seminar on mathematical problem solving. The attitudes of representative sample of 12 of the tea

zzz [600]

Answer:

a) 1.9

b) 3.25

c) 1.5

d) -5.25

Step-by-step explanation:

We are given the following in the data:

4, 7, -1, 1, 0, 5, -3, 2, -1, 6, 5, -2

a) Mean change score

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{23}{12} = 1.9$

b) standard deviation for this population

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}$

where $x_i$ are data points, $\bar{x}$ is the mean and n is the number of observations.

Sum of differences = 126.92

$S.D = \sqrt{\dfrac{126.92}{12}} = 3.25$

c) median change score

Sorted data: -3, -2, -1, -1, 0, 1, 2, 4, 5, 5, 6, 7

$Median:\\\text{If n is odd, then}\\\\Median = \displaystyle\frac{n+1}{2}th ~term \\\\\text{If n is even, then}\\\\Median = \displaystyle\frac{\frac{n}{2}th~term + (\frac{n}{2}+1)th~term}{2}$

$\text{Median} = \dfrac{6^{th}+7^{th}}{2} = \dfrac{1+2}{2} = 1.5$

d) change score that is 2.2 standard deviations below the mean.

$\mu - 2.2(\sigma)\\1.92 - 2.2(3.25) = -5.25$

3 0

3 years ago